Sequences

Least number m such that 4^m == +- 1 (mod 4n + 1).

Least number m such that 5^m == +- 1 (mod 5n + 1).

Least number m such that 6^m == +- 1 (mod 6n + 1).

Least number m such that 7^m == +- 1 (mod 7n + 1).

Least number m such that 8^m == +- 1 (mod 8n + 1).

Least number m such that 9^m == +- 1 (mod 9n + 1).

Least number m such that 10^m == +- 1 mod (10n + 1).

Least number m such that 11^m == +- 1 (mod 11n + 1).

Least number m such that 12^m == +- 1 (mod 12n + 1).

For n>0, a(n) = least positive number m such that 4^m == +1 or -1 (mod 2n + 1), with a(0) = 0 by convention.

For n>0, a(n) = least positive number m such that 8^m == +1 or -1 (mod 2n + 1), with a(0) = 0 by convention.

Order of 3 mod 3n+1.

Order of 3 mod 3n+2.

Order of 4 mod 4n+1.

Order of 4 mod 4n-1.

Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=3.

Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=4.

Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=5.

Dowling numbers: e.g.f. exp(x + (exp(b*x) - 1)/b), with b=6.

Dowling numbers: e.g.f. exp(x + (exp(b*x) - 1)/b), with b=7.

Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=8.

Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=9.

Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=10.

a(n) = (n+2)*2^(2*n-1) - (n/2)*binomial(2*n,n).

Unicursal (i.e., possessing an Eulerian path) planar rooted maps with n edges.

Odd numbers that are not of the form x^2 + y^2 + 10*z^2.

3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.

Roman numerals with 1 letter, in numerical order; then those with 2 letters, etc.

Roman numerals with 1 letter, in alphabetical order; then those with 2 letters, etc.

a(n) has the property that the sequence b(n) = number of 2's between successive 3's is the same as the original sequence.

Rows of Pascal's triangle written as a single number.

Numbers of form 2^i*7^j, with i, j >= 0.

Numbers of the form 2^i*5^j with i, j >= 0.

Numbers of the form 3^i*5^j with i, j >= 0.

Numbers of the form 3^i*7^j with i, j >= 0.

Numbers of the form 5^i*7^j with i, j >= 0.

Numbers of the form 2^i * 11^j.

Numbers of the form 3^i*11^j.

Numbers of the form 5^i * 11^j.

Numbers of the form 7^i*11^j.

Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6 (n > 0).

Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j)).

Kimberling's paraphrase of the binary number system: if n = (2k-1)*2^m then a(n) = k.

Fractal sequence obtained from Fibonacci numbers (or Wythoff array).

Number of primes <= n!.

Unique monotonic sequence of nonnegative integers satisfying a(a(n)) = 3n.

a(n) = number of types of conjugacy classes in GL(n,q) (this is independent of q).

Location of 0's when natural numbers are listed in binary.

Add 4, then reverse digits; start with 0.

Symmetries in planted (1,3) trees on 2n vertices.